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A160296 Numerator of Hermite(n, 19/30). 1
1, 19, -89, -18791, -236879, 29323099, 1090116631, -58460151311, -4544610262559, 124108949730979, 20763741608252551, -163979183232607031, -105896125442269661039, -1126538793947045592341, 598088096752283650823671, 18460868240159776597398049 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
LINKS
FORMULA
From G. C. Greubel, Oct 03 2018: (Start)
a(n) = 15^n * Hermite(n, 19/30).
E.g.f.: exp(19*x - 225*x^2).
a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(19/15)^(n-2*k)/(k!*(n-2*k)!)). (End)
EXAMPLE
Numerators of 1, 19/15, -89/225, -18791/3375, -236879/50625, ...
MATHEMATICA
Numerator[HermiteH[Range[0, 20], 19/30]] (* Harvey P. Dale, Sep 10 2011 *)
Table[15^n*HermiteH[n, 19/30], {n, 0, 30}] (* G. C. Greubel, Oct 03 2018 *)
PROG
(PARI) a(n)=numerator(polhermite(n, 19/30)) \\ Charles R Greathouse IV, Jan 29 2016
(PARI) x='x+O('x^30); Vec(serlaplace(exp(19*x - 225*x^2))) \\ G. C. Greubel, Oct 03 2018
(Magma) [Numerator((&+[(-1)^k*Factorial(n)*(19/15)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Oct 03 2018
CROSSREFS
Cf. A001024 (denominators).
Sequence in context: A124947 A126406 A201306 * A347364 A224097 A088574
KEYWORD
sign,frac
AUTHOR
N. J. A. Sloane, Nov 12 2009
STATUS
approved

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Last modified March 28 05:02 EDT 2024. Contains 371235 sequences. (Running on oeis4.)